45. a) 9x²-1- (3x - 2)² = 0; б) x + (5x + 2)² = 25(1 + x²); в) (2x - 3)² - 2x(4 + 2x) = 11; г) (4x - 3)(3 + 4x) - 2x(8x - 1) = 0. 2 46. a) (x - 1)(x + 1) = 2(x - 3)² - x²; 2 б) (2x + 3)² - 4(x - 1)(x + 1) = 49; в) 3(х + 5)² - 4x² = (2-x)(2 + x); г) (3x + 1)² - (3x - 2)(2 + 3x) = 17.

Решаю уравнения.

45. a)

$$9x^2 - 1 - (3x - 2)^2 = 0$$

$$9x^2 - 1 - (9x^2 - 12x + 4) = 0$$

$$9x^2 - 1 - 9x^2 + 12x - 4 = 0$$

$$12x - 5 = 0$$

$$12x = 5$$

$$x = \frac{5}{12}$$

Ответ: $$x = \frac{5}{12}$$

45. б)

$$x + (5x + 2)^2 = 25(1 + x^2)$$ $$x + 25x^2 + 20x + 4 = 25 + 25x^2$$ $$21x = 21$$ $$x = 1$$

Ответ: $$x = 1$$

45. в)

$$(2x - 3)^2 - 2x(4 + 2x) = 11$$ $$4x^2 - 12x + 9 - 8x - 4x^2 = 11$$ $$-20x = 2$$ $$x = -\frac{1}{10}$$

Ответ: $$x = -\frac{1}{10}$$

45. г)

$$(4x - 3)(3 + 4x) - 2x(8x - 1) = 0$$ $$16x^2 - 9 - 16x^2 + 2x = 0$$ $$2x = 9$$ $$x = \frac{9}{2} = 4.5$$

Ответ: $$x = 4.5$$

46. a)

$$(x - 1)(x + 1) = 2(x - 3)^2 - x^2$$ $$x^2 - 1 = 2(x^2 - 6x + 9) - x^2$$ $$x^2 - 1 = 2x^2 - 12x + 18 - x^2$$ $$x^2 - 1 = x^2 - 12x + 18$$ $$12x = 19$$ $$x = \frac{19}{12}$$

Ответ: $$x = \frac{19}{12}$$

46. б)

$$(2x + 3)^2 - 4(x - 1)(x + 1) = 49$$ $$4x^2 + 12x + 9 - 4(x^2 - 1) = 49$$ $$4x^2 + 12x + 9 - 4x^2 + 4 = 49$$ $$12x = 36$$ $$x = 3$$

Ответ: $$x = 3$$

46. в)

$$3(x + 5)^2 - 4x^2 = (2-x)(2 + x)$$ $$3(x^2 + 10x + 25) - 4x^2 = 4 - x^2$$ $$3x^2 + 30x + 75 - 4x^2 = 4 - x^2$$ $$-x^2 + 30x + 75 = 4 - x^2$$ $$30x = -71$$ $$x = -\frac{71}{30}$$

Ответ: $$x = -\frac{71}{30}$$

46. г)

$$(3x + 1)^2 - (3x - 2)(2 + 3x) = 17$$ $$9x^2 + 6x + 1 - (9x^2 - 4x - 4) = 17$$ $$9x^2 + 6x + 1 - 9x^2 + 4x + 4 = 17$$ $$10x = 12$$ $$x = \frac{6}{5} = 1.2$$

Ответ: $$x = 1.2$$